Adaptive rational block Arnoldi methods for model reductions in large-scale MIMO dynamical systems

Year 2016, Volume: 4 Issue: 2, 227 - 239, 01.03.2016

Oussama Abidi Mustapha Hached Khalide Jbilou

Abstract

In recent years, a great interest
has been shown towards Krylov subspace techniques applied to model order
reduction of large-scale dynamical systems. A special interest has been devoted
to single-input single-output (SISO) systems by using moment matching
techniques based on Arnoldi or Lanczos algorithms. In this paper, we consider
multiple-input multiple-output (MIMO) dynamical systems and introduce the
rational block Arnoldi process to design low order dynamical systems that are
close in some sense to the original MIMO dynamical system. Rational Krylov
subspace methods are based on the choice of suitable shifts that are selected a
priori or adaptively. In this paper, we propose an adaptive selection of those
shifts and show the efficiency of this approach in our numerical tests. We also
give some new block Arnoldi-like relations that are used to propose an upper
bound for the norm of the error on the transfer function.

Keywords

Dynamical systems, model reduction, rational block Krylov subspaces

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